In Cool Water by the Sons of the Pioneers, it appears to be the actual name of the horse:

Old Dan and I
With throats burned dry
And souls that cry
For water

But in the traditional range ballad I Ride an Old Paint, it appears to be a generic term and to apply to the same horse that has already been identified as a "Paint."

I ride an old paint,
I lead an old dan
I'm going to Montana
For to throw the Hoolian

A "paint" is apparently a type of pinto, or perhaps just another name for a pinto, which makes sense given that pinto probably comes from the Latin pinctus, meaning "painted." It's a horse that looks like somebody threw a bucket over it.

Wiki says:
"Cool Water" is a song written in 1936 by Bob Nolan. It is about a man and his mule, Dan, and a mirage in the desert.

The lyrics seem to confirm this:

Quote:

"All day I face the barren waste without the taste of water,
Cool water.
Old Dan and I with throats burned dry and souls that cry for water,
Cool water.

The night are cool and I'm a fool each stars a pool of water,
Cool water.
But with the dawn I'll wake and yawn and carry on to water,
Cool water.

Keep a movin' Dan, don't you listen to him Dan, he's a devil not a man
and he spreads the burnin' sand with water.
Dan can't you see that big green tree where the waters runnin' free
and it's waiting there for me and you."

Wiki says:
"Cool Water" is a song written in 1936 by Bob Nolan. It is about a man and his mule, Dan, and a mirage in the desert.

The lyrics seem to confirm this:

I don't see anything in the lyrics which clarifies whether Dan is a mule or a horse. Wikipedia's source seems to be an unattributed claim on a random website. However, it does look unlikely that calling the beast "Dan" had anything to do with there be a so-named type of horse, unless as mrpayday suggested, it's a corruption of "dun". Do mules come in dun?

... But in the traditional range ballad I Ride an Old Paint, it appears to be a generic term and to apply to the same horse that has already been identified as a "Paint."

I ride an old paint,
I lead an old dan
I'm going to Montana
For to throw the Hoolian

Boy it's a good thing I don't read the lyrics before I start singin' 'em. I sing it

I ride an old paint,
I lead an old dam.
I'm goin' to Montana
For to throw the Houlihan...

Namely, his pack horse is a mare. And if you're curious about "Houlihan" it's a lariat throw to hobble the front legs of a wild horse, kind of akin to the throw a heeler makes in team roping in rodeo, except snaring the front legs instead of the hind legs; so our cowboy is off to Montana to catch wild horses for a living.

I've heard a number of versions, and I'm pretty sure 'dan' is what people are actually saying, but 'dam' makes more sense. It's an actual meaningful term in animal lore -- since, unlike 'dan' I can actually find a definition of it that has to do with horses. The change suggests that it happened through oral tradition to better fit the rhyme with 'Hoolihan'.

Quote:

Originally Posted by MonkeyMensch

And if you're curious about "Houlihan" it's a lariat throw to hobble the front legs of a wild horse, kind of akin to the throw a heeler makes in team roping in rodeo, except snaring the front legs instead of the hind legs; so our cowboy is off to Montana to catch wild horses for a living.

I had actually assumed he meant to join a specific ranch belonging to some Irishman that would turn out to have been famous, when I got around to looking into it. Further research on your point led me to Mudcat (I had forgotten about that site). There are diverse and sourced explanations for the term, including ones having to do with an actual lasso technique. Some say the loop is supposed to drop over the head, which apparently keeps the horses from getting spooked. Some say the loop its supposed to come up from under to snag a head that the horse has been holding down because apparently that's the way they run in a corral.

So, depending on the definition you go with, it may not be wild horses he was after, but the next line does fit well with that notion:

Quote:

They feed in the coulies, they water in the draw

"Coulie" and "draw" seem, near as I can tell, interchangeable terms for ditches carved out by flowing water. Under my own assumption that the song was talking about driving cattle, this would mean places they stopped for water. But if we're talking about wild horses, then this is more like a bit of horse-hunter lore. That also may make some sense out of the next line:

Quote:

Their tails are all matted, their backs are all raw

If we're talking about cows, why would their backs be raw? But horses that had escaped from some ranch might still bear the evidence of their saddles. Then again, this may be assuming more than is needed by way of explanation: they apparently had in those days a kind of corral called a remuda (from the Latin re + mūtāre, to change) from which cowhands used to change out horses. It would make sense that you'd use this Hooli'an to get your horse for the day, and so the term "throw the Hoolihan" could just imply your basic cowboying, as in "I throwed the hoolihan nigh twenty hears at the old Circle-Schwa Ranch."

I think he means the paint and the dan have raw backs and matted tails. Meaning that the they've been traveling without rest for a long time, maybe he's switching out horses every now and then. He hasn't had time to stop and tend to them properly.

Agree old paint is a pinto colored horse and and old dan is his pack horse or mule, not the horse's name. "You don't put a name on something you might have to eat one day."
Hoolihan or Hooley-Ann is a method either plain or fancy for throwing a lasso.
Cow or dogies backs are raw because of too vigorous use of a whip and tails are matted because of close proximity to a cows rear end and burrs and other debris being caught in the hairs.
I believe fiery refers to the cook and the snuffy could be the trail boss or foreman of the cattle drive.
You don't ride any horse you depend on until their backs are raw.